There are 1 questions in this calculation: for each question, the 1 derivative of x is calculated.
    Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ first\ derivative\ of\ function\ {(2{({x}^{2} + 1)}^{2}{\frac{1}{({x}^{2} + \frac{1}{2})}}^{2})}^{\frac{1}{2}}{(2{(1 + \frac{1}{(4{x}^{2})})}^{2}{\frac{1}{((\frac{1}{(4{x}^{2})}) + \frac{1}{2})}}^{2})}^{\frac{1}{2}}((x + \frac{1}{(2x)}){\frac{1}{({(x + \frac{1}{(2x)})}^{2} + \frac{1}{4})}}^{\frac{1}{2}})\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = \frac{(\frac{2x^{4}}{(x^{2} + \frac{1}{2})^{2}} + \frac{4x^{2}}{(x^{2} + \frac{1}{2})^{2}} + \frac{2}{(x^{2} + \frac{1}{2})^{2}})^{\frac{1}{2}}(\frac{\frac{1}{8}}{(\frac{\frac{1}{4}}{x^{2}} + \frac{1}{2})^{2}x^{4}} + \frac{1}{(\frac{\frac{1}{4}}{x^{2}} + \frac{1}{2})^{2}x^{2}} + \frac{2}{(\frac{\frac{1}{4}}{x^{2}} + \frac{1}{2})^{2}})^{\frac{1}{2}}x}{(x^{2} + \frac{\frac{1}{4}}{x^{2}} + \frac{5}{4})^{\frac{1}{2}}} + \frac{\frac{1}{2}(\frac{2x^{4}}{(x^{2} + \frac{1}{2})^{2}} + \frac{4x^{2}}{(x^{2} + \frac{1}{2})^{2}} + \frac{2}{(x^{2} + \frac{1}{2})^{2}})^{\frac{1}{2}}(\frac{\frac{1}{8}}{(\frac{\frac{1}{4}}{x^{2}} + \frac{1}{2})^{2}x^{4}} + \frac{1}{(\frac{\frac{1}{4}}{x^{2}} + \frac{1}{2})^{2}x^{2}} + \frac{2}{(\frac{\frac{1}{4}}{x^{2}} + \frac{1}{2})^{2}})^{\frac{1}{2}}}{(x^{2} + \frac{\frac{1}{4}}{x^{2}} + \frac{5}{4})^{\frac{1}{2}}x}\\&\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( \frac{(\frac{2x^{4}}{(x^{2} + \frac{1}{2})^{2}} + \frac{4x^{2}}{(x^{2} + \frac{1}{2})^{2}} + \frac{2}{(x^{2} + \frac{1}{2})^{2}})^{\frac{1}{2}}(\frac{\frac{1}{8}}{(\frac{\frac{1}{4}}{x^{2}} + \frac{1}{2})^{2}x^{4}} + \frac{1}{(\frac{\frac{1}{4}}{x^{2}} + \frac{1}{2})^{2}x^{2}} + \frac{2}{(\frac{\frac{1}{4}}{x^{2}} + \frac{1}{2})^{2}})^{\frac{1}{2}}x}{(x^{2} + \frac{\frac{1}{4}}{x^{2}} + \frac{5}{4})^{\frac{1}{2}}} + \frac{\frac{1}{2}(\frac{2x^{4}}{(x^{2} + \frac{1}{2})^{2}} + \frac{4x^{2}}{(x^{2} + \frac{1}{2})^{2}} + \frac{2}{(x^{2} + \frac{1}{2})^{2}})^{\frac{1}{2}}(\frac{\frac{1}{8}}{(\frac{\frac{1}{4}}{x^{2}} + \frac{1}{2})^{2}x^{4}} + \frac{1}{(\frac{\frac{1}{4}}{x^{2}} + \frac{1}{2})^{2}x^{2}} + \frac{2}{(\frac{\frac{1}{4}}{x^{2}} + \frac{1}{2})^{2}})^{\frac{1}{2}}}{(x^{2} + \frac{\frac{1}{4}}{x^{2}} + \frac{5}{4})^{\frac{1}{2}}x}\right)}{dx}\\=&\frac{(\frac{\frac{1}{2}(2(\frac{-2(2x + 0)}{(x^{2} + \frac{1}{2})^{3}})x^{4} + \frac{2*4x^{3}}{(x^{2} + \frac{1}{2})^{2}} + 4(\frac{-2(2x + 0)}{(x^{2} + \frac{1}{2})^{3}})x^{2} + \frac{4*2x}{(x^{2} + \frac{1}{2})^{2}} + 2(\frac{-2(2x + 0)}{(x^{2} + \frac{1}{2})^{3}}))}{(\frac{2x^{4}}{(x^{2} + \frac{1}{2})^{2}} + \frac{4x^{2}}{(x^{2} + \frac{1}{2})^{2}} + \frac{2}{(x^{2} + \frac{1}{2})^{2}})^{\frac{1}{2}}})(\frac{\frac{1}{8}}{(\frac{\frac{1}{4}}{x^{2}} + \frac{1}{2})^{2}x^{4}} + \frac{1}{(\frac{\frac{1}{4}}{x^{2}} + \frac{1}{2})^{2}x^{2}} + \frac{2}{(\frac{\frac{1}{4}}{x^{2}} + \frac{1}{2})^{2}})^{\frac{1}{2}}x}{(x^{2} + \frac{\frac{1}{4}}{x^{2}} + \frac{5}{4})^{\frac{1}{2}}} + \frac{(\frac{2x^{4}}{(x^{2} + \frac{1}{2})^{2}} + \frac{4x^{2}}{(x^{2} + \frac{1}{2})^{2}} + \frac{2}{(x^{2} + \frac{1}{2})^{2}})^{\frac{1}{2}}(\frac{\frac{1}{2}(\frac{\frac{1}{8}(\frac{-2(\frac{\frac{1}{4}*-2}{x^{3}} + 0)}{(\frac{\frac{1}{4}}{x^{2}} + \frac{1}{2})^{3}})}{x^{4}} + \frac{\frac{1}{8}*-4}{(\frac{\frac{1}{4}}{x^{2}} + \frac{1}{2})^{2}x^{5}} + \frac{(\frac{-2(\frac{\frac{1}{4}*-2}{x^{3}} + 0)}{(\frac{\frac{1}{4}}{x^{2}} + \frac{1}{2})^{3}})}{x^{2}} + \frac{-2}{(\frac{\frac{1}{4}}{x^{2}} + \frac{1}{2})^{2}x^{3}} + 2(\frac{-2(\frac{\frac{1}{4}*-2}{x^{3}} + 0)}{(\frac{\frac{1}{4}}{x^{2}} + \frac{1}{2})^{3}}))}{(\frac{\frac{1}{8}}{(\frac{\frac{1}{4}}{x^{2}} + \frac{1}{2})^{2}x^{4}} + \frac{1}{(\frac{\frac{1}{4}}{x^{2}} + \frac{1}{2})^{2}x^{2}} + \frac{2}{(\frac{\frac{1}{4}}{x^{2}} + \frac{1}{2})^{2}})^{\frac{1}{2}}})x}{(x^{2} + \frac{\frac{1}{4}}{x^{2}} + \frac{5}{4})^{\frac{1}{2}}} + (\frac{2x^{4}}{(x^{2} + \frac{1}{2})^{2}} + \frac{4x^{2}}{(x^{2} + \frac{1}{2})^{2}} + \frac{2}{(x^{2} + \frac{1}{2})^{2}})^{\frac{1}{2}}(\frac{\frac{1}{8}}{(\frac{\frac{1}{4}}{x^{2}} + \frac{1}{2})^{2}x^{4}} + \frac{1}{(\frac{\frac{1}{4}}{x^{2}} + \frac{1}{2})^{2}x^{2}} + \frac{2}{(\frac{\frac{1}{4}}{x^{2}} + \frac{1}{2})^{2}})^{\frac{1}{2}}(\frac{\frac{-1}{2}(2x + \frac{\frac{1}{4}*-2}{x^{3}} + 0)}{(x^{2} + \frac{\frac{1}{4}}{x^{2}} + \frac{5}{4})^{\frac{3}{2}}})x + \frac{(\frac{2x^{4}}{(x^{2} + \frac{1}{2})^{2}} + \frac{4x^{2}}{(x^{2} + \frac{1}{2})^{2}} + \frac{2}{(x^{2} + \frac{1}{2})^{2}})^{\frac{1}{2}}(\frac{\frac{1}{8}}{(\frac{\frac{1}{4}}{x^{2}} + \frac{1}{2})^{2}x^{4}} + \frac{1}{(\frac{\frac{1}{4}}{x^{2}} + \frac{1}{2})^{2}x^{2}} + \frac{2}{(\frac{\frac{1}{4}}{x^{2}} + \frac{1}{2})^{2}})^{\frac{1}{2}}}{(x^{2} + \frac{\frac{1}{4}}{x^{2}} + \frac{5}{4})^{\frac{1}{2}}} + \frac{\frac{1}{2}(\frac{\frac{1}{2}(2(\frac{-2(2x + 0)}{(x^{2} + \frac{1}{2})^{3}})x^{4} + \frac{2*4x^{3}}{(x^{2} + \frac{1}{2})^{2}} + 4(\frac{-2(2x + 0)}{(x^{2} + \frac{1}{2})^{3}})x^{2} + \frac{4*2x}{(x^{2} + \frac{1}{2})^{2}} + 2(\frac{-2(2x + 0)}{(x^{2} + \frac{1}{2})^{3}}))}{(\frac{2x^{4}}{(x^{2} + \frac{1}{2})^{2}} + \frac{4x^{2}}{(x^{2} + \frac{1}{2})^{2}} + \frac{2}{(x^{2} + \frac{1}{2})^{2}})^{\frac{1}{2}}})(\frac{\frac{1}{8}}{(\frac{\frac{1}{4}}{x^{2}} + \frac{1}{2})^{2}x^{4}} + \frac{1}{(\frac{\frac{1}{4}}{x^{2}} + \frac{1}{2})^{2}x^{2}} + \frac{2}{(\frac{\frac{1}{4}}{x^{2}} + \frac{1}{2})^{2}})^{\frac{1}{2}}}{(x^{2} + \frac{\frac{1}{4}}{x^{2}} + \frac{5}{4})^{\frac{1}{2}}x} + \frac{\frac{1}{2}(\frac{2x^{4}}{(x^{2} + \frac{1}{2})^{2}} + \frac{4x^{2}}{(x^{2} + \frac{1}{2})^{2}} + \frac{2}{(x^{2} + \frac{1}{2})^{2}})^{\frac{1}{2}}(\frac{\frac{1}{2}(\frac{\frac{1}{8}(\frac{-2(\frac{\frac{1}{4}*-2}{x^{3}} + 0)}{(\frac{\frac{1}{4}}{x^{2}} + \frac{1}{2})^{3}})}{x^{4}} + \frac{\frac{1}{8}*-4}{(\frac{\frac{1}{4}}{x^{2}} + \frac{1}{2})^{2}x^{5}} + \frac{(\frac{-2(\frac{\frac{1}{4}*-2}{x^{3}} + 0)}{(\frac{\frac{1}{4}}{x^{2}} + \frac{1}{2})^{3}})}{x^{2}} + \frac{-2}{(\frac{\frac{1}{4}}{x^{2}} + \frac{1}{2})^{2}x^{3}} + 2(\frac{-2(\frac{\frac{1}{4}*-2}{x^{3}} + 0)}{(\frac{\frac{1}{4}}{x^{2}} + \frac{1}{2})^{3}}))}{(\frac{\frac{1}{8}}{(\frac{\frac{1}{4}}{x^{2}} + \frac{1}{2})^{2}x^{4}} + \frac{1}{(\frac{\frac{1}{4}}{x^{2}} + \frac{1}{2})^{2}x^{2}} + \frac{2}{(\frac{\frac{1}{4}}{x^{2}} + \frac{1}{2})^{2}})^{\frac{1}{2}}})}{(x^{2} + \frac{\frac{1}{4}}{x^{2}} + \frac{5}{4})^{\frac{1}{2}}x} + \frac{\frac{1}{2}(\frac{2x^{4}}{(x^{2} + \frac{1}{2})^{2}} + \frac{4x^{2}}{(x^{2} + \frac{1}{2})^{2}} + \frac{2}{(x^{2} + \frac{1}{2})^{2}})^{\frac{1}{2}}(\frac{\frac{1}{8}}{(\frac{\frac{1}{4}}{x^{2}} + \frac{1}{2})^{2}x^{4}} + \frac{1}{(\frac{\frac{1}{4}}{x^{2}} + \frac{1}{2})^{2}x^{2}} + \frac{2}{(\frac{\frac{1}{4}}{x^{2}} + \frac{1}{2})^{2}})^{\frac{1}{2}}(\frac{\frac{-1}{2}(2x + \frac{\frac{1}{4}*-2}{x^{3}} + 0)}{(x^{2} + \frac{\frac{1}{4}}{x^{2}} + \frac{5}{4})^{\frac{3}{2}}})}{x} + \frac{\frac{1}{2}(\frac{2x^{4}}{(x^{2} + \frac{1}{2})^{2}} + \frac{4x^{2}}{(x^{2} + \frac{1}{2})^{2}} + \frac{2}{(x^{2} + \frac{1}{2})^{2}})^{\frac{1}{2}}(\frac{\frac{1}{8}}{(\frac{\frac{1}{4}}{x^{2}} + \frac{1}{2})^{2}x^{4}} + \frac{1}{(\frac{\frac{1}{4}}{x^{2}} + \frac{1}{2})^{2}x^{2}} + \frac{2}{(\frac{\frac{1}{4}}{x^{2}} + \frac{1}{2})^{2}})^{\frac{1}{2}}*-1}{(x^{2} + \frac{\frac{1}{4}}{x^{2}} + \frac{5}{4})^{\frac{1}{2}}x^{2}}\\=&\frac{-4(\frac{\frac{1}{8}}{(\frac{\frac{1}{4}}{x^{2}} + \frac{1}{2})^{2}x^{4}} + \frac{1}{(\frac{\frac{1}{4}}{x^{2}} + \frac{1}{2})^{2}x^{2}} + \frac{2}{(\frac{\frac{1}{4}}{x^{2}} + \frac{1}{2})^{2}})^{\frac{1}{2}}x^{6}}{(\frac{2x^{4}}{(x^{2} + \frac{1}{2})^{2}} + \frac{4x^{2}}{(x^{2} + \frac{1}{2})^{2}} + \frac{2}{(x^{2} + \frac{1}{2})^{2}})^{\frac{1}{2}}(x^{2} + \frac{1}{2})^{3}(x^{2} + \frac{\frac{1}{4}}{x^{2}} + \frac{5}{4})^{\frac{1}{2}}} + \frac{4(\frac{\frac{1}{8}}{(\frac{\frac{1}{4}}{x^{2}} + \frac{1}{2})^{2}x^{4}} + \frac{1}{(\frac{\frac{1}{4}}{x^{2}} + \frac{1}{2})^{2}x^{2}} + \frac{2}{(\frac{\frac{1}{4}}{x^{2}} + \frac{1}{2})^{2}})^{\frac{1}{2}}x^{4}}{(\frac{2x^{4}}{(x^{2} + \frac{1}{2})^{2}} + \frac{4x^{2}}{(x^{2} + \frac{1}{2})^{2}} + \frac{2}{(x^{2} + \frac{1}{2})^{2}})^{\frac{1}{2}}(x^{2} + \frac{1}{2})^{2}(x^{2} + \frac{\frac{1}{4}}{x^{2}} + \frac{5}{4})^{\frac{1}{2}}} - \frac{10(\frac{\frac{1}{8}}{(\frac{\frac{1}{4}}{x^{2}} + \frac{1}{2})^{2}x^{4}} + \frac{1}{(\frac{\frac{1}{4}}{x^{2}} + \frac{1}{2})^{2}x^{2}} + \frac{2}{(\frac{\frac{1}{4}}{x^{2}} + \frac{1}{2})^{2}})^{\frac{1}{2}}x^{4}}{(\frac{2x^{4}}{(x^{2} + \frac{1}{2})^{2}} + \frac{4x^{2}}{(x^{2} + \frac{1}{2})^{2}} + \frac{2}{(x^{2} + \frac{1}{2})^{2}})^{\frac{1}{2}}(x^{2} + \frac{1}{2})^{3}(x^{2} + \frac{\frac{1}{4}}{x^{2}} + \frac{5}{4})^{\frac{1}{2}}} + \frac{6(\frac{\frac{1}{8}}{(\frac{\frac{1}{4}}{x^{2}} + \frac{1}{2})^{2}x^{4}} + \frac{1}{(\frac{\frac{1}{4}}{x^{2}} + \frac{1}{2})^{2}x^{2}} + \frac{2}{(\frac{\frac{1}{4}}{x^{2}} + \frac{1}{2})^{2}})^{\frac{1}{2}}x^{2}}{(\frac{2x^{4}}{(x^{2} + \frac{1}{2})^{2}} + \frac{4x^{2}}{(x^{2} + \frac{1}{2})^{2}} + \frac{2}{(x^{2} + \frac{1}{2})^{2}})^{\frac{1}{2}}(x^{2} + \frac{1}{2})^{2}(x^{2} + \frac{\frac{1}{4}}{x^{2}} + \frac{5}{4})^{\frac{1}{2}}} - \frac{8(\frac{\frac{1}{8}}{(\frac{\frac{1}{4}}{x^{2}} + \frac{1}{2})^{2}x^{4}} + \frac{1}{(\frac{\frac{1}{4}}{x^{2}} + \frac{1}{2})^{2}x^{2}} + \frac{2}{(\frac{\frac{1}{4}}{x^{2}} + \frac{1}{2})^{2}})^{\frac{1}{2}}x^{2}}{(\frac{2x^{4}}{(x^{2} + \frac{1}{2})^{2}} + \frac{4x^{2}}{(x^{2} + \frac{1}{2})^{2}} + \frac{2}{(x^{2} + \frac{1}{2})^{2}})^{\frac{1}{2}}(x^{2} + \frac{1}{2})^{3}(x^{2} + \frac{\frac{1}{4}}{x^{2}} + \frac{5}{4})^{\frac{1}{2}}} + \frac{5(\frac{2x^{4}}{(x^{2} + \frac{1}{2})^{2}} + \frac{4x^{2}}{(x^{2} + \frac{1}{2})^{2}} + \frac{2}{(x^{2} + \frac{1}{2})^{2}})^{\frac{1}{2}}}{16(\frac{\frac{1}{8}}{(\frac{\frac{1}{4}}{x^{2}} + \frac{1}{2})^{2}x^{4}} + \frac{1}{(\frac{\frac{1}{4}}{x^{2}} + \frac{1}{2})^{2}x^{2}} + \frac{2}{(\frac{\frac{1}{4}}{x^{2}} + \frac{1}{2})^{2}})^{\frac{1}{2}}(\frac{\frac{1}{4}}{x^{2}} + \frac{1}{2})^{3}(x^{2} + \frac{\frac{1}{4}}{x^{2}} + \frac{5}{4})^{\frac{1}{2}}x^{6}} - \frac{3(\frac{2x^{4}}{(x^{2} + \frac{1}{2})^{2}} + \frac{4x^{2}}{(x^{2} + \frac{1}{2})^{2}} + \frac{2}{(x^{2} + \frac{1}{2})^{2}})^{\frac{1}{2}}}{4(\frac{\frac{1}{8}}{(\frac{\frac{1}{4}}{x^{2}} + \frac{1}{2})^{2}x^{4}} + \frac{1}{(\frac{\frac{1}{4}}{x^{2}} + \frac{1}{2})^{2}x^{2}} + \frac{2}{(\frac{\frac{1}{4}}{x^{2}} + \frac{1}{2})^{2}})^{\frac{1}{2}}(\frac{\frac{1}{4}}{x^{2}} + \frac{1}{2})^{2}(x^{2} + \frac{\frac{1}{4}}{x^{2}} + \frac{5}{4})^{\frac{1}{2}}x^{4}} + \frac{(\frac{2x^{4}}{(x^{2} + \frac{1}{2})^{2}} + \frac{4x^{2}}{(x^{2} + \frac{1}{2})^{2}} + \frac{2}{(x^{2} + \frac{1}{2})^{2}})^{\frac{1}{2}}}{(\frac{\frac{1}{8}}{(\frac{\frac{1}{4}}{x^{2}} + \frac{1}{2})^{2}x^{4}} + \frac{1}{(\frac{\frac{1}{4}}{x^{2}} + \frac{1}{2})^{2}x^{2}} + \frac{2}{(\frac{\frac{1}{4}}{x^{2}} + \frac{1}{2})^{2}})^{\frac{1}{2}}(\frac{\frac{1}{4}}{x^{2}} + \frac{1}{2})^{3}(x^{2} + \frac{\frac{1}{4}}{x^{2}} + \frac{5}{4})^{\frac{1}{2}}x^{4}} - \frac{(\frac{2x^{4}}{(x^{2} + \frac{1}{2})^{2}} + \frac{4x^{2}}{(x^{2} + \frac{1}{2})^{2}} + \frac{2}{(x^{2} + \frac{1}{2})^{2}})^{\frac{1}{2}}}{(\frac{\frac{1}{8}}{(\frac{\frac{1}{4}}{x^{2}} + \frac{1}{2})^{2}x^{4}} + \frac{1}{(\frac{\frac{1}{4}}{x^{2}} + \frac{1}{2})^{2}x^{2}} + \frac{2}{(\frac{\frac{1}{4}}{x^{2}} + \frac{1}{2})^{2}})^{\frac{1}{2}}(\frac{\frac{1}{4}}{x^{2}} + \frac{1}{2})^{2}(x^{2} + \frac{\frac{1}{4}}{x^{2}} + \frac{5}{4})^{\frac{1}{2}}x^{2}} + \frac{(\frac{2x^{4}}{(x^{2} + \frac{1}{2})^{2}} + \frac{4x^{2}}{(x^{2} + \frac{1}{2})^{2}} + \frac{2}{(x^{2} + \frac{1}{2})^{2}})^{\frac{1}{2}}}{(\frac{\frac{1}{8}}{(\frac{\frac{1}{4}}{x^{2}} + \frac{1}{2})^{2}x^{4}} + \frac{1}{(\frac{\frac{1}{4}}{x^{2}} + \frac{1}{2})^{2}x^{2}} + \frac{2}{(\frac{\frac{1}{4}}{x^{2}} + \frac{1}{2})^{2}})^{\frac{1}{2}}(\frac{\frac{1}{4}}{x^{2}} + \frac{1}{2})^{3}(x^{2} + \frac{\frac{1}{4}}{x^{2}} + \frac{5}{4})^{\frac{1}{2}}x^{2}} - \frac{(\frac{2x^{4}}{(x^{2} + \frac{1}{2})^{2}} + \frac{4x^{2}}{(x^{2} + \frac{1}{2})^{2}} + \frac{2}{(x^{2} + \frac{1}{2})^{2}})^{\frac{1}{2}}(\frac{\frac{1}{8}}{(\frac{\frac{1}{4}}{x^{2}} + \frac{1}{2})^{2}x^{4}} + \frac{1}{(\frac{\frac{1}{4}}{x^{2}} + \frac{1}{2})^{2}x^{2}} + \frac{2}{(\frac{\frac{1}{4}}{x^{2}} + \frac{1}{2})^{2}})^{\frac{1}{2}}x^{2}}{(x^{2} + \frac{\frac{1}{4}}{x^{2}} + \frac{5}{4})^{\frac{3}{2}}} + \frac{(\frac{2x^{4}}{(x^{2} + \frac{1}{2})^{2}} + \frac{4x^{2}}{(x^{2} + \frac{1}{2})^{2}} + \frac{2}{(x^{2} + \frac{1}{2})^{2}})^{\frac{1}{2}}(\frac{\frac{1}{8}}{(\frac{\frac{1}{4}}{x^{2}} + \frac{1}{2})^{2}x^{4}} + \frac{1}{(\frac{\frac{1}{4}}{x^{2}} + \frac{1}{2})^{2}x^{2}} + \frac{2}{(\frac{\frac{1}{4}}{x^{2}} + \frac{1}{2})^{2}})^{\frac{1}{2}}}{4(x^{2} + \frac{\frac{1}{4}}{x^{2}} + \frac{5}{4})^{\frac{3}{2}}x^{2}} - \frac{(\frac{\frac{1}{8}}{(\frac{\frac{1}{4}}{x^{2}} + \frac{1}{2})^{2}x^{4}} + \frac{1}{(\frac{\frac{1}{4}}{x^{2}} + \frac{1}{2})^{2}x^{2}} + \frac{2}{(\frac{\frac{1}{4}}{x^{2}} + \frac{1}{2})^{2}})^{\frac{1}{2}}(\frac{2x^{4}}{(x^{2} + \frac{1}{2})^{2}} + \frac{4x^{2}}{(x^{2} + \frac{1}{2})^{2}} + \frac{2}{(x^{2} + \frac{1}{2})^{2}})^{\frac{1}{2}}}{2(x^{2} + \frac{\frac{1}{4}}{x^{2}} + \frac{5}{4})^{\frac{1}{2}}x^{2}} + \frac{(\frac{2x^{4}}{(x^{2} + \frac{1}{2})^{2}} + \frac{4x^{2}}{(x^{2} + \frac{1}{2})^{2}} + \frac{2}{(x^{2} + \frac{1}{2})^{2}})^{\frac{1}{2}}}{32(\frac{\frac{1}{8}}{(\frac{\frac{1}{4}}{x^{2}} + \frac{1}{2})^{2}x^{4}} + \frac{1}{(\frac{\frac{1}{4}}{x^{2}} + \frac{1}{2})^{2}x^{2}} + \frac{2}{(\frac{\frac{1}{4}}{x^{2}} + \frac{1}{2})^{2}})^{\frac{1}{2}}(\frac{\frac{1}{4}}{x^{2}} + \frac{1}{2})^{3}(x^{2} + \frac{\frac{1}{4}}{x^{2}} + \frac{5}{4})^{\frac{1}{2}}x^{8}} - \frac{(\frac{2x^{4}}{(x^{2} + \frac{1}{2})^{2}} + \frac{4x^{2}}{(x^{2} + \frac{1}{2})^{2}} + \frac{2}{(x^{2} + \frac{1}{2})^{2}})^{\frac{1}{2}}}{8(\frac{\frac{1}{8}}{(\frac{\frac{1}{4}}{x^{2}} + \frac{1}{2})^{2}x^{4}} + \frac{1}{(\frac{\frac{1}{4}}{x^{2}} + \frac{1}{2})^{2}x^{2}} + \frac{2}{(\frac{\frac{1}{4}}{x^{2}} + \frac{1}{2})^{2}})^{\frac{1}{2}}(\frac{\frac{1}{4}}{x^{2}} + \frac{1}{2})^{2}(x^{2} + \frac{\frac{1}{4}}{x^{2}} + \frac{5}{4})^{\frac{1}{2}}x^{6}} + \frac{2(\frac{\frac{1}{8}}{(\frac{\frac{1}{4}}{x^{2}} + \frac{1}{2})^{2}x^{4}} + \frac{1}{(\frac{\frac{1}{4}}{x^{2}} + \frac{1}{2})^{2}x^{2}} + \frac{2}{(\frac{\frac{1}{4}}{x^{2}} + \frac{1}{2})^{2}})^{\frac{1}{2}}}{(\frac{2x^{4}}{(x^{2} + \frac{1}{2})^{2}} + \frac{4x^{2}}{(x^{2} + \frac{1}{2})^{2}} + \frac{2}{(x^{2} + \frac{1}{2})^{2}})^{\frac{1}{2}}(x^{2} + \frac{1}{2})^{2}(x^{2} + \frac{\frac{1}{4}}{x^{2}} + \frac{5}{4})^{\frac{1}{2}}} - \frac{2(\frac{\frac{1}{8}}{(\frac{\frac{1}{4}}{x^{2}} + \frac{1}{2})^{2}x^{4}} + \frac{1}{(\frac{\frac{1}{4}}{x^{2}} + \frac{1}{2})^{2}x^{2}} + \frac{2}{(\frac{\frac{1}{4}}{x^{2}} + \frac{1}{2})^{2}})^{\frac{1}{2}}}{(\frac{2x^{4}}{(x^{2} + \frac{1}{2})^{2}} + \frac{4x^{2}}{(x^{2} + \frac{1}{2})^{2}} + \frac{2}{(x^{2} + \frac{1}{2})^{2}})^{\frac{1}{2}}(x^{2} + \frac{1}{2})^{3}(x^{2} + \frac{\frac{1}{4}}{x^{2}} + \frac{5}{4})^{\frac{1}{2}}} + \frac{(\frac{2x^{4}}{(x^{2} + \frac{1}{2})^{2}} + \frac{4x^{2}}{(x^{2} + \frac{1}{2})^{2}} + \frac{2}{(x^{2} + \frac{1}{2})^{2}})^{\frac{1}{2}}(\frac{\frac{1}{8}}{(\frac{\frac{1}{4}}{x^{2}} + \frac{1}{2})^{2}x^{4}} + \frac{1}{(\frac{\frac{1}{4}}{x^{2}} + \frac{1}{2})^{2}x^{2}} + \frac{2}{(\frac{\frac{1}{4}}{x^{2}} + \frac{1}{2})^{2}})^{\frac{1}{2}}}{8(x^{2} + \frac{\frac{1}{4}}{x^{2}} + \frac{5}{4})^{\frac{3}{2}}x^{4}} - \frac{(\frac{2x^{4}}{(x^{2} + \frac{1}{2})^{2}} + \frac{4x^{2}}{(x^{2} + \frac{1}{2})^{2}} + \frac{2}{(x^{2} + \frac{1}{2})^{2}})^{\frac{1}{2}}(\frac{\frac{1}{8}}{(\frac{\frac{1}{4}}{x^{2}} + \frac{1}{2})^{2}x^{4}} + \frac{1}{(\frac{\frac{1}{4}}{x^{2}} + \frac{1}{2})^{2}x^{2}} + \frac{2}{(\frac{\frac{1}{4}}{x^{2}} + \frac{1}{2})^{2}})^{\frac{1}{2}}}{2(x^{2} + \frac{\frac{1}{4}}{x^{2}} + \frac{5}{4})^{\frac{3}{2}}} + \frac{(\frac{2x^{4}}{(x^{2} + \frac{1}{2})^{2}} + \frac{4x^{2}}{(x^{2} + \frac{1}{2})^{2}} + \frac{2}{(x^{2} + \frac{1}{2})^{2}})^{\frac{1}{2}}(\frac{\frac{1}{8}}{(\frac{\frac{1}{4}}{x^{2}} + \frac{1}{2})^{2}x^{4}} + \frac{1}{(\frac{\frac{1}{4}}{x^{2}} + \frac{1}{2})^{2}x^{2}} + \frac{2}{(\frac{\frac{1}{4}}{x^{2}} + \frac{1}{2})^{2}})^{\frac{1}{2}}}{(x^{2} + \frac{\frac{1}{4}}{x^{2}} + \frac{5}{4})^{\frac{1}{2}}}\\ \end{split}\end{equation} \]

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